Using Matlab and the Guitar String script codes that I have supplied in eLearning. Modify the...
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Using Matlab and the Guitar String script codes that I have supplied in eLearning. Modify the script to show the mode oscillations for the guitar string presented in the lecture on Monday. You should modify the program, publish the output and combine the pdf files generated into a single pdf file and submit that to eLearning for the following cases: Case 1: Oscillations for the first vibration mode. Case 2: Oscillations for the second vibration mode. Case 3: Oscillations for the third vibration mode. Case 4: Oscillations for the fifth vibration mode - all oscillations for the fourth mode are zero. Case 5: Oscillations for the combinations of modes 1 through 5. clear all clc syms x t m yc Cn Dn lambda n Physical properties of the string L = 1; c = 660; alpha = 20; beta = 2*alpha/ (c^2); lambda (n) (c*n*pi/L) *sqrt (1 N=50; Number of Fourier series terms (vibration modes) *Define the initial offset and the initial velocity fs (x) =piecewise (0<x<=0.25, (-2/250) *x, 0.25<x<=1, (2/(1000*L-250)) *x- (2*L)/(1000*L-250)); gs (x)=0*x; * Calculate the C and D coefficients of the solution Cn (n) = (2/L) *int (fs (x) *sin ( (n*pi/L) *x),x, 0, L); Dn (n) = (2/ (lambda (n) *L) ) *int ((gs (x) +alpha*fs (x) ) * sin((n*pi/L) *x),x, 0, L); fprintf('The Cn (n) fprintf('The Dn (n) * Put the Fourier Series solution for the string together Fourier_freqs (x, t) = subs ((Cn (n) *cos (lambda (n) *t) +Dn (n) *sin (lambda (n) *t)) *sin ( (n*pi/L) *x),n,1:N); f(x, t) = sum (Fourier_freqs (x, t)); plot (x1, yl) ] (beta^2*c^2*L^2) / (4*pi^2*n^2)); Plot the initial offset for the string x1 = 0:0.01:1; yl = f (x1, 0); - end coefficient is %s \n \n', simplify (Cn (n))) coefficient is %s \n \n', simplify (Dn (n))) axis ([01 -0.0025 0.0025]) xlabel ('x'); grid on grid minor pause (0.01) m Calculate the string function for times greater than zero for m 1:11 y3 (m, :) = single (f(x1, m* 0.0001) *exp(-alpha*0.0001*m)); end Plot the string functions for times greater than zero for n 1:11 plot (x1, yl, xl, y3 (n, :)) axis ( [0 1 -0.0025 0.0025]) xlabel ('x'); grid on grid minor pause (0.01); Using Matlab and the Guitar String script codes that I have supplied in eLearning. Modify the script to show the mode oscillations for the guitar string presented in the lecture on Monday. You should modify the program, publish the output and combine the pdf files generated into a single pdf file and submit that to eLearning for the following cases: Case 1: Oscillations for the first vibration mode. Case 2: Oscillations for the second vibration mode. Case 3: Oscillations for the third vibration mode. Case 4: Oscillations for the fifth vibration mode - all oscillations for the fourth mode are zero. Case 5: Oscillations for the combinations of modes 1 through 5. clear all clc syms x t m yc Cn Dn lambda n Physical properties of the string L = 1; c = 660; alpha = 20; beta = 2*alpha/ (c^2); lambda (n) (c*n*pi/L) *sqrt (1 N=50; Number of Fourier series terms (vibration modes) *Define the initial offset and the initial velocity fs (x) =piecewise (0<x<=0.25, (-2/250) *x, 0.25<x<=1, (2/(1000*L-250)) *x- (2*L)/(1000*L-250)); gs (x)=0*x; * Calculate the C and D coefficients of the solution Cn (n) = (2/L) *int (fs (x) *sin ( (n*pi/L) *x),x, 0, L); Dn (n) = (2/ (lambda (n) *L) ) *int ((gs (x) +alpha*fs (x) ) * sin((n*pi/L) *x),x, 0, L); fprintf('The Cn (n) fprintf('The Dn (n) * Put the Fourier Series solution for the string together Fourier_freqs (x, t) = subs ((Cn (n) *cos (lambda (n) *t) +Dn (n) *sin (lambda (n) *t)) *sin ( (n*pi/L) *x),n,1:N); f(x, t) = sum (Fourier_freqs (x, t)); plot (x1, yl) ] (beta^2*c^2*L^2) / (4*pi^2*n^2)); Plot the initial offset for the string x1 = 0:0.01:1; yl = f (x1, 0); - end coefficient is %s \n \n', simplify (Cn (n))) coefficient is %s \n \n', simplify (Dn (n))) axis ([01 -0.0025 0.0025]) xlabel ('x'); grid on grid minor pause (0.01) m Calculate the string function for times greater than zero for m 1:11 y3 (m, :) = single (f(x1, m* 0.0001) *exp(-alpha*0.0001*m)); end Plot the string functions for times greater than zero for n 1:11 plot (x1, yl, xl, y3 (n, :)) axis ( [0 1 -0.0025 0.0025]) xlabel ('x'); grid on grid minor pause (0.01);
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Case 1 Oscillations for the first vibration mode matlab Modify the loop for time iterations to run o... View the full answer
Related Book For
Intermediate Accounting
ISBN: 978-1118147290
15th edition
Authors: Donald E. Kieso, Jerry J. Weygandt, and Terry D. Warfield
Posted Date:
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